Question: Solve for $x$, ignoring any extraneous solutions: $\dfrac{x^2 + 10}{x - 7} = \dfrac{17x - 60}{x - 7}$
Multiply both sides by $x - 7$ $ \dfrac{x^2 + 10}{x - 7} (x - 7) = \dfrac{17x - 60}{x - 7} (x - 7)$ $ x^2 + 10 = 17x - 60$ Subtract $17x - 60$ from both sides: $ x^2 + 10 - (17x - 60) = 17x - 60 - (17x - 60)$ $ x^2 + 10 - 17x + 60 = 0$ $ x^2 + 70 - 17x = 0$ Factor the expression: $ (x - 10)(x - 7) = 0$ Therefore $x = 10$ or $x = 7$ However, the original expression is undefined when $x = 7$. Therefore, the only solution is $x = 10$.